Question: Simplify the following expression: $x = \dfrac{3n^2 + 36n + 60}{n + 2} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $3$ , so we can rewrite the expression: $ x =\dfrac{3(n^2 + 12n + 20)}{n + 2} $ Then we factor the remaining polynomial: $n^2 + {12}n + {20} $ ${2} + {10} = {12}$ ${2} \times {10} = {20}$ $ (n + {2}) (n + {10}) $ This gives us a factored expression: $\dfrac{3(n + {2}) (n + {10})}{n + 2}$ We can divide the numerator and denominator by $(n - 2)$ on condition that $n \neq -2$ Therefore $x = 3(n + 10); n \neq -2$